On the peripheral spectrum of order continuous, positive operators (Q1977741)

Let \(X\) be an normed space ordered by a closed cone \(K\) with a non-empty interior. Let \(K'\) be the dual cone. The assumptions on \(K\) imply that the cone \(K'\) has a base \(B\). The authors say that a linear continuous positive operator \(A:X\to X\) satisfies the maximum principle if for each \(x>0\) there exists a functional \(f\in B\) such that \(f(x)> 0\) and \(f(Ax)= \sup\{g(Ax): g\in B\}\). The paper is devoted to a rather detailed study of this property which is pertinent to many applied situations.